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 Documentation Ver 1.0.0 August 2011 by
 <a href="http://mmc.geofisica.unam.mx/luiggi">Luis M. de la Cruz</a> <br>
 <a href="http://mmc.geofisica.unam.mx"> GMMC </a> -
 <a href="http://www.geofisica.unam.mx/recnat/"> Depto. de Recursos Naturales </a> -
 <a href="http://www.geofisica.unam.mx"> Instituto de Geof&iacute;sica </a> -
 <a href="http://www.unam.mx"> UNAM </a><br>
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<div class="title">Examples/03Laplace/hoffman.cpp</div>  </div>
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<a href="hoffman_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 
<a name="l00032"></a>00032 <span class="preprocessor">#include &lt;iostream&gt;</span>
<a name="l00033"></a>00033 <span class="preprocessor">#include &lt;cmath&gt;</span>
<a name="l00034"></a>00034 <span class="preprocessor">#include &quot;Meshes/StructuredMesh.hpp&quot;</span>
<a name="l00035"></a>00035 <span class="preprocessor">#include &quot;Meshes/Uniform.hpp&quot;</span>
<a name="l00036"></a>00036 <span class="preprocessor">#include &quot;Equations/ScalarEquation.hpp&quot;</span>
<a name="l00037"></a>00037 <span class="preprocessor">#include &quot;Schemes/LaplaceScheme.hpp&quot;</span>
<a name="l00038"></a>00038 <span class="preprocessor">#include &quot;Solvers/TDMA.hpp&quot;</span>
<a name="l00039"></a>00039 <span class="preprocessor">#include &quot;Utils/num_utils.hpp&quot;</span>
<a name="l00040"></a>00040 <span class="preprocessor">#include &quot;Utils/inout.hpp&quot;</span> 
<a name="l00041"></a>00041 <span class="preprocessor">#include &quot;Utils/GNUplot.hpp&quot;</span>
<a name="l00042"></a>00042 <span class="keyword">using namespace </span>Tuna;
<a name="l00043"></a>00043 
<a name="l00044"></a>00044 <span class="comment">// Scalar field in two dimension</span>
<a name="l00045"></a>00045 <span class="keyword">typedef</span> <a class="code" href="structTuna_1_1TunaArray.html#af3bcab5018eec3d7697c9fb03ad89157" title="Definition of big arrays to store scalar fields on meshes.">TunaArray&lt;double, 2&gt;::huge</a> ScalarField2D;
<a name="l00046"></a>00046 
<a name="l00047"></a>00047 <span class="keywordtype">void</span> exactSolution(ScalarField2D &amp;T, <span class="keywordtype">double</span> hx, <span class="keywordtype">double</span> hy, <span class="keywordtype">double</span> A,
<a name="l00048"></a>00048                    <span class="keywordtype">double</span> dx, <span class="keywordtype">double</span> dy)
<a name="l00049"></a>00049 {
<a name="l00050"></a>00050   <span class="keywordtype">double</span> x, y, c1, s1, s2, s3, sum, exact;
<a name="l00051"></a>00051   <span class="keywordtype">int</span> Nmax = 20;
<a name="l00052"></a>00052   <span class="keywordtype">int</span> NI = T.ubound(firstDim);
<a name="l00053"></a>00053   <span class="keywordtype">int</span> NJ = T.ubound(secondDim);
<a name="l00054"></a>00054   
<a name="l00055"></a>00055   <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i = 1; i &lt; NI; ++i)
<a name="l00056"></a>00056     <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j = 1; j &lt; NJ; ++j) {
<a name="l00057"></a>00057       sum = 0.0;
<a name="l00058"></a>00058       <span class="keywordflow">for</span>(<span class="keywordtype">int</span> n = 1; n &lt; Nmax; n += 2) {
<a name="l00059"></a>00059         x = i * dx;
<a name="l00060"></a>00060         y = j * dy;
<a name="l00061"></a>00061         c1 = 2.0 / (n * PI);
<a name="l00062"></a>00062                 s1 = sinh( n * PI * (hy - y) / hx );
<a name="l00063"></a>00063                 s2 = sinh( n * PI * hy / hx);
<a name="l00064"></a>00064                 s3 = sin( n * PI * x / hx);
<a name="l00065"></a>00065                 sum += c1 * s1 * s3 / s2;
<a name="l00066"></a>00066       }
<a name="l00067"></a>00067       T(i,j) = 2.0 * A * sum ;
<a name="l00068"></a>00068     }
<a name="l00069"></a>00069 }
<a name="l00070"></a>00070 
<a name="l00071"></a>00071 <span class="keywordtype">int</span> main() 
<a name="l00072"></a>00072 {
<a name="l00073"></a>00073   <span class="keywordtype">double</span> length_x, length_y, Amp;
<a name="l00074"></a>00074   <span class="keywordtype">int</span> num_nodes_x, num_nodes_y;
<a name="l00075"></a>00075   <span class="keywordtype">double</span> tolerance;    
<a name="l00076"></a>00076   <span class="keywordtype">int</span> tdma_iter;
<a name="l00077"></a>00077   <a class="code" href="structTuna_1_1timer.html" title="Struct useful to measure the elapsed time.">timer</a> time;
<a name="l00078"></a>00078   
<a name="l00079"></a>00079 <span class="comment">// Reading data from the input file</span>
<a name="l00080"></a>00080   std::ifstream input_cin (<span class="stringliteral">&quot;input_hoffman&quot;</span>); 
<a name="l00081"></a>00081   input_cin &gt;&gt; length_x;
<a name="l00082"></a>00082   input_cin &gt;&gt; length_y;
<a name="l00083"></a>00083   input_cin &gt;&gt; num_nodes_x; 
<a name="l00084"></a>00084   input_cin &gt;&gt; num_nodes_y; 
<a name="l00085"></a>00085   input_cin &gt;&gt; Amp; 
<a name="l00086"></a>00086   input_cin &gt;&gt; tdma_iter;
<a name="l00087"></a>00087   input_cin &gt;&gt; tolerance;
<a name="l00088"></a>00088   input_cin.close();
<a name="l00089"></a>00089 
<a name="l00090"></a>00090   std::cout.precision(10);
<a name="l00091"></a>00091   std::cout.setf(ios_base::fixed,ios_base::floatfield);
<a name="l00092"></a>00092 
<a name="l00093"></a>00093   <a class="code" href="classTuna_1_1StructuredMesh.html" title="General structured meshes on rectangular domains.">StructuredMesh&lt;Uniform&lt;double, 2&gt;</a> &gt; mesh(length_x, num_nodes_x,
<a name="l00094"></a>00094                                            length_y, num_nodes_y);
<a name="l00095"></a>00095   <span class="keywordtype">double</span> dx = mesh.getDelta(X);
<a name="l00096"></a>00096   <span class="keywordtype">double</span> dy = mesh.getDelta(Y);
<a name="l00097"></a>00097   mesh.print();
<a name="l00098"></a>00098 
<a name="l00099"></a>00099   ScalarField2D T (mesh.getExtentVolumes());
<a name="l00100"></a>00100   ScalarField2D Ta(mesh.getExtentVolumes());
<a name="l00101"></a>00101   ScalarField2D Tn(mesh.getExtentNodes());
<a name="l00102"></a>00102   
<a name="l00103"></a>00103   Range all = Range::all();
<a name="l00104"></a>00104   Tn(all, Tn.lbound(secondDim)) = Amp;
<a name="l00105"></a>00105   InOut::writeToFile(Tn, 0, <span class="stringliteral">&quot;./DataHoffman/temp.&quot;</span>, dx, dy);
<a name="l00106"></a>00106   NumUtils::interpolateToVolumes(T, Tn);
<a name="l00107"></a>00107   
<a name="l00108"></a>00108   exactSolution(Tn, length_x, length_y, Amp, dx, dy);
<a name="l00109"></a>00109   InOut::writeToFile(Tn, 0, <span class="stringliteral">&quot;./DataHoffman/exac.&quot;</span>, dx, dy);
<a name="l00110"></a>00110   NumUtils::interpolateToVolumes(Ta, Tn);
<a name="l00111"></a>00111  
<a name="l00112"></a>00112 <span class="preprocessor">#ifdef WITH_GNUPLOT</span>
<a name="l00113"></a>00113 <span class="preprocessor"></span>    GNUplot plotter;
<a name="l00114"></a>00114     plotter(<span class="stringliteral">&quot;set grid&quot;</span>);
<a name="l00115"></a>00115     plotter(<span class="stringliteral">&quot;set contour&quot;</span>);
<a name="l00116"></a>00116     plotter(<span class="stringliteral">&quot;set view 60,45,1,1&quot;</span>);
<a name="l00117"></a>00117     plotter(<span class="stringliteral">&quot;set ticslevel 1.5&quot;</span>);
<a name="l00118"></a>00118     plotter(<span class="stringliteral">&quot;set cntrparam level discrete 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95&quot;</span>);
<a name="l00119"></a>00119     plotter(<span class="stringliteral">&quot;splot [0:1][0:2][0:100] \&quot;./DataHoffman/exac.00000\&quot; title \&quot;Exact solution\&quot; w l&quot;</span>);
<a name="l00120"></a>00120     std::cout &lt;&lt; <span class="stringliteral">&quot;\n &gt;---&gt; Press &lt;1&gt; and then &lt;enter&gt; to continue \n&quot;</span>;
<a name="l00121"></a>00121     <span class="keywordtype">int</span> pause; std::cin &gt;&gt; pause;
<a name="l00122"></a>00122     plotter(<span class="stringliteral">&quot;splot [0:1][0:2][0:100] \&quot;./DataHoffman/temp.00000\&quot; title \&quot;Initial conditions\&quot;w l&quot;</span>);
<a name="l00123"></a>00123     std::cout &lt;&lt; <span class="stringliteral">&quot;\n &gt;---&gt; Press &lt;1&gt; and then &lt;enter&gt; to continue \n&quot;</span>;
<a name="l00124"></a>00124     std::cin &gt;&gt; pause;
<a name="l00125"></a>00125 <span class="preprocessor">#endif</span>
<a name="l00126"></a>00126 <span class="preprocessor"></span>
<a name="l00127"></a>00127     SparseMatrix&lt; Diagonal&lt;double, 2&gt; &gt; A(num_nodes_x, num_nodes_y); 
<a name="l00128"></a>00128 
<a name="l00129"></a>00129     ScalarField2D             b(num_nodes_x, num_nodes_y);
<a name="l00130"></a>00130   
<a name="l00131"></a>00131     <a class="code" href="classTuna_1_1ScalarEquation.html" title="This class derives from GeneralEquation through B &amp; N trick.">ScalarEquation&lt; LaplaceScheme&lt;double, 2&gt;</a> &gt; laplace(T, A, b,
<a name="l00132"></a>00132                                                        mesh.getDeltas());
<a name="l00133"></a>00133     laplace.<a class="code" href="classTuna_1_1GeneralEquation.html#a25136e525b1fe03af821d085080d4992" title="Setup Dirichlet boundary conditions on walls.">setDirichlet</a>(TOP_WALL);
<a name="l00134"></a>00134     laplace.setDirichlet(BOTTOM_WALL);
<a name="l00135"></a>00135     laplace.setDirichlet(LEFT_WALL);
<a name="l00136"></a>00136     laplace.setDirichlet(RIGHT_WALL);
<a name="l00137"></a>00137     laplace.setGamma(1.0);
<a name="l00138"></a>00138     laplace.print();
<a name="l00139"></a>00139 
<a name="l00140"></a>00140     time.<a class="code" href="structTuna_1_1timer.html#a5b0cf85d5db9b941e13ce7c79d7de7b0" title="Start the clock.">tic</a>();        
<a name="l00141"></a>00141     laplace.calcCoefficients();
<a name="l00142"></a>00142     <span class="keywordtype">int</span> iter = Solver::TDMA2DY(laplace, tolerance, tdma_iter);
<a name="l00143"></a>00143     std::cout &lt;&lt; <span class="stringliteral">&quot;\n Elapsed time for solving Ax = b : &quot;</span> 
<a name="l00144"></a>00144               &lt;&lt; time.<a class="code" href="structTuna_1_1timer.html#a3796592dd5b589521e1093d9225eee5e" title="Stop the clock and returns the elapsed time.">toc</a>() &lt;&lt; <span class="stringliteral">&quot; seconds \n\n&quot;</span>;   
<a name="l00145"></a>00145     
<a name="l00146"></a>00146     std::cout &lt;&lt; <span class="stringliteral">&quot;\n Iterations = &quot;</span> &lt;&lt; iter
<a name="l00147"></a>00147               &lt;&lt; <span class="stringliteral">&quot;\t Residual = &quot;</span> &lt;&lt; laplace.getResidual();
<a name="l00148"></a>00148 
<a name="l00149"></a>00149     laplace.update();  
<a name="l00150"></a>00150     NumUtils::interpolateToNodes(Tn, T);
<a name="l00151"></a>00151     InOut::writeToFile(Tn, 1, <span class="stringliteral">&quot;./DataHoffman/temp.&quot;</span>, dx, dy);
<a name="l00152"></a>00152 
<a name="l00153"></a>00153     cout &lt;&lt; <span class="stringliteral">&quot;\n\n Error L1  = &quot;</span> &lt;&lt; NumUtils::calcErrorL1( T, Ta )
<a name="l00154"></a>00154          &lt;&lt; <span class="stringliteral">&quot;\t Error RMS = &quot;</span> &lt;&lt; NumUtils::calcErrorL2( T, Ta );
<a name="l00155"></a>00155 
<a name="l00156"></a>00156     <span class="keywordtype">double</span> ReL1, ReL2, ReLmax;
<a name="l00157"></a>00157     <span class="keywordtype">double</span> AeL1, AeL2, AeLmax;
<a name="l00158"></a>00158     <span class="keywordtype">double</span> NL1, NL2, NLmax;
<a name="l00159"></a>00159     NL1 = NumUtils::normL1(Ta);
<a name="l00160"></a>00160     NL2 = NumUtils::normL2(Ta);
<a name="l00161"></a>00161     NLmax = NumUtils::normLmax(Ta);
<a name="l00162"></a>00162 
<a name="l00163"></a>00163     AeL1 = NumUtils::calcAbsoluteError_L1( T, Ta);
<a name="l00164"></a>00164     AeL2 = NumUtils::calcAbsoluteError_L2( T, Ta);
<a name="l00165"></a>00165     AeLmax = NumUtils::calcAbsoluteError_Lmax( T, Ta);
<a name="l00166"></a>00166     ReL1 = AeL1 / NL1;
<a name="l00167"></a>00167     ReL2 = AeL2 / NL2;
<a name="l00168"></a>00168     ReLmax = AeLmax / NLmax;
<a name="l00169"></a>00169     
<a name="l00170"></a>00170     cout &lt;&lt; <span class="stringliteral">&quot;\n Error L1  Absolute = &quot;</span> &lt;&lt; AeL1
<a name="l00171"></a>00171          &lt;&lt; <span class="stringliteral">&quot;\t Relative = &quot;</span> &lt;&lt; ReL1
<a name="l00172"></a>00172          &lt;&lt; <span class="stringliteral">&quot;\t Norm = &quot;</span> &lt;&lt; NL1;
<a name="l00173"></a>00173 
<a name="l00174"></a>00174     cout &lt;&lt; <span class="stringliteral">&quot;\n Error L2  Absolute = &quot;</span> &lt;&lt; AeL2
<a name="l00175"></a>00175          &lt;&lt; <span class="stringliteral">&quot;\t Relative = &quot;</span> &lt;&lt; ReL2
<a name="l00176"></a>00176          &lt;&lt; <span class="stringliteral">&quot;\t Norm = &quot;</span> &lt;&lt; NL2;
<a name="l00177"></a>00177 
<a name="l00178"></a>00178     cout &lt;&lt; <span class="stringliteral">&quot;\n Error Lmax  Absolute = &quot;</span> &lt;&lt; AeLmax
<a name="l00179"></a>00179          &lt;&lt; <span class="stringliteral">&quot;\t Relative = &quot;</span> &lt;&lt; ReLmax
<a name="l00180"></a>00180          &lt;&lt; <span class="stringliteral">&quot;\t Norm = &quot;</span> &lt;&lt; NLmax;
<a name="l00181"></a>00181 
<a name="l00182"></a>00182     <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i = 0; i &lt;= T.ubound(firstDim); ++i)
<a name="l00183"></a>00183       <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j = 0; j &lt;= T.ubound(secondDim); ++j) {
<a name="l00184"></a>00184         T(i,j) = abs(T(i,j) - Ta(i,j));
<a name="l00185"></a>00185       }
<a name="l00186"></a>00186 
<a name="l00187"></a>00187     
<a name="l00188"></a>00188  
<a name="l00189"></a>00189     NumUtils::interpolateToNodes(Tn, T);           
<a name="l00190"></a>00190     InOut::writeToFile(Tn, 0, <span class="stringliteral">&quot;./DataHoffman/erro.&quot;</span>, dx, dy);
<a name="l00191"></a>00191     
<a name="l00192"></a>00192 <span class="preprocessor">#ifdef WITH_GNUPLOT</span>
<a name="l00193"></a>00193 <span class="preprocessor"></span>    plotter(<span class="stringliteral">&quot;splot [0:1][0:2][0:100] \&quot;./DataHoffman/temp.00001\&quot; title \&quot;Numerical Solution\&quot; w l&quot;</span>);
<a name="l00194"></a>00194     std::cout &lt;&lt; <span class="stringliteral">&quot;\n &gt;---&gt; Press &lt;1&gt; and then &lt;enter&gt; to continue \n&quot;</span>;
<a name="l00195"></a>00195     std::cin &gt;&gt; pause;
<a name="l00196"></a>00196     plotter(<span class="stringliteral">&quot;splot [0:1][0:2][0:100] \&quot;./DataHoffman/erro.00000\&quot; title \&quot;Error\&quot; w l&quot;</span>);
<a name="l00197"></a>00197     std::cout &lt;&lt; <span class="stringliteral">&quot;\n &gt;---&gt; Press &lt;1&gt; and then &lt;enter&gt; to continue \n&quot;</span>;
<a name="l00198"></a>00198     std::cin &gt;&gt; pause;
<a name="l00199"></a>00199 <span class="preprocessor">#endif</span>
<a name="l00200"></a>00200 <span class="preprocessor"></span>    
<a name="l00201"></a>00201     <span class="keywordflow">return</span> 0;
<a name="l00202"></a>00202 }
<a name="l00203"></a>00203 
<a name="l00204"></a>00204 
<a name="l00205"></a>00205 
<a name="l00206"></a>00206 
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